I would say you bring the debts, car maintenance, the food shopping all into the family pot.
It would make more sense to use savings to clear the debts (assuming that won't leave you with no savings for rainy days) but you increase what your DH puts in the joint account each month to cover repaying the savings (transfer each month day after his money hits the joint account), and half the food bills (or whatever division seems fair given the differences in your wages) and something towards car maintenance. Whats left is 'fun money' and ideally you have strict rules that the joint account debt card can only be used in supermarkets.
Also have a family rule that nothing is put on the credit cards that can't be paid off out of the current or next month's 'fun money' budget without both agreeing it. (so a boiler break down, ok, an extra fancy shirt, not)
As a family, that will at least mean you aren't wasting money on interest payments or paying late fees if he's not paying off his debts properly each month. It also means you can start budgeting for MOTs etc, and as it's joint money paying for cars, you get a say.
You have decided to share your life with this man, so you have to start acting like a unit. This doesn't mean you have to have just one joint account with both of you spending 'fun money' out of it, but it does mean for house hold bills (which cars are), they need to be joint responsiblity - both in paying and agreeing to take on in the first place. His debts aren't just his problem, but if you are going to pay them then you have a say in if they are run up again.
If he doesn't want to do this, then I would think very carefully about bringing another child into a relationship where you have vastly different approaches to money. 2 DCs are a lot more expensive than 1 to fund on your own, and it does sound like eventually, even if you share a house with him still, you will be funding them on your own.